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In the above cases I want to find the acceleration a for m1. I can do it by considering m1 and m2 to be a system, which would give me a = F/(m1+m2). How can I use a free-body diagram instead to calculate the acceleration? Using a free-body diagram, m2 only affects the vertical motion by exerting a vertical force and not the horizontal acceleration but we know that since the mass of the system has increased the acceleration will decrease. TLDR; how would I solve for the acceleration of m1 in both of the above cases using only a free-body diagram. All surfaces are frictionless.